Details

analyze3.9s (13.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	62.4%	12.6%	8
31.2%	56.2%	12.6%	9
34.3%	53%	12.6%	10
42.9%	44.5%	12.6%	11
46.8%	40.6%	12.6%	12
47.8%	39.6%	12.6%	13
52.6%	34.8%	12.6%	14

Compiler

Compiled 25 to 20 computations (20% saved)

sample570.0ms (2%)

Algorithm

1×

intervals

Results

120.0ms	53×	body	1024	valid
97.0ms	43×	body	1024	invalid
46.0ms	156×	body	128	valid
35.0ms	24×	body	512	valid
29.0ms	20×	body	512	invalid
28.0ms	7×	body	2048	valid
12.0ms	16×	body	256	valid
8.0ms	27×	body	128	invalid
8.0ms	9×	body	256	invalid

Compiler

Compiled 52 to 42 computations (19.2% saved)

simplify152.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1078×	`sqr-pow_binary64`
786×	`cube-prod_binary64`
770×	`fabs-mul_binary64`
484×	`unswap-sqr_binary64`
392×	`pow-sqr_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	34
1	30	34
2	66	34
3	124	34
4	217	34
5	465	34
6	669	34
7	1130	34
8	1177	34
9	1369	34
10	1574	34
11	1868	34
12	2152	34
13	2573	34
14	3206	34
15	3520	34
16	3872	34
17	4026	34
18	4094	34
19	4136	34
20	4933	34
21	4905	34

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

21.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))

Compiler

Compiled 72 to 57 computations (20.8% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)
✓	0.3b	(*.f64 (PI.f64) (/.f64 angle 180))
✓	24.4b	(sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))
✓	24.7b	(cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))

series78.0ms (0.3%)

Counts

4 → 60

Calls

4 calls:

58.0ms	(pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)
7.0ms	(sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))
7.0ms	(cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))
6.0ms	(*.f64 (PI.f64) (/.f64 angle 180))

rewrite29.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
12×	`add-exp-log_binary64`

Counts

4 → 72

Calls

4 calls:

13.0ms	(*.f64 (PI.f64) (/.f64 angle 180))
6.0ms	(pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)
2.0ms	(cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))
2.0ms	(sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))

simplify163.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

600×	`fma-neg_binary64`
587×	`times-frac_binary64`
403×	`*-commutative_binary64`
321×	`fma-def_binary64`
249×	`cancel-sign-sub-inv_binary64`

Counts

132 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	196	2107
1	448	2003
2	1447	1981
3	3580	1967
4	4922	1967
5	4939	1967

prune833.0ms (2.9%)

Pruning

35 alts after pruning (35 fresh and 0 done)

	Pruned	Kept	Total
New	117	35	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	35	153

Error

19.4b

Counts

153 → 35

Alt Table

Status	Error	Program
	21.5b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (/.f64 (.f64 (cbrt.f64 angle) (cbrt.f64 angle)) (sqrt.f64 180))) (/.f64 (cbrt.f64 angle) (sqrt.f64 180))))) 2))
	30.7b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (log.f64 (exp.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 (PI.f64) (.f64 (cbrt.f64 180) (cbrt.f64 180))) (/.f64 angle (cbrt.f64 180))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 (/.f64 angle 180))) (sqrt.f64 (/.f64 angle 180))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	30.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 angle 180)) 3)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
▶	20.8b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.4b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 (/.f64 angle 180)) (cbrt.f64 (/.f64 angle 180)))) (cbrt.f64 (/.f64 angle 180))))) 2))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cbrt.f64 (.f64 (.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	44.6b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (*.f64 b (sin.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 (/.f64 angle 180)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (log.f64 (exp.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (expm1.f64 (log1p.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.4b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180))))) 2))
	33.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (.f64 (.f64 b b) (-.f64 (.f64 (.f64 (.f64 angle angle) (pow.f64 (PI.f64) 2)) 1/32400) (.f64 (*.f64 (pow.f64 angle 4) (pow.f64 (PI.f64) 4)) 1/3149280000))))
	21.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)) (cbrt.f64 (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))) (cbrt.f64 (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (/.f64 (sqrt.f64 angle) (sqrt.f64 180))) (/.f64 (sqrt.f64 angle) (sqrt.f64 180))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	24.7b	(+.f64 (pow.f64 (.f64 a (cos.f64 (expm1.f64 (log1p.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	33.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (-.f64 (.f64 1/32400 (.f64 (pow.f64 angle 2) (.f64 (pow.f64 (PI.f64) 2) (pow.f64 b 2)))) (.f64 1/3149280000 (.f64 (pow.f64 angle 4) (.f64 (pow.f64 (PI.f64) 4) (pow.f64 b 2))))))
	22.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (exp.f64 (log.f64 (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 angle) (cbrt.f64 angle))) (/.f64 (cbrt.f64 angle) 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (/.f64 (.f64 (PI.f64) angle) 180))) 2))
	37.5b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)))
	21.4b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 angle) (cbrt.f64 angle))) (/.f64 (cbrt.f64 angle) 180)))) 2))
	44.4b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (.f64 (sqrt.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (sqrt.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2))
	27.4b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64)))) 2)))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (/.f64 (.f64 (cbrt.f64 angle) (cbrt.f64 angle)) (sqrt.f64 180))) (/.f64 (cbrt.f64 angle) (sqrt.f64 180))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	25.8b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (.f64 1/180 (*.f64 angle (PI.f64)))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (*.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 angle (sqrt.f64 180))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 (/.f64 angle 180)) (cbrt.f64 (/.f64 angle 180)))) (cbrt.f64 (/.f64 angle 180))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	44.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 angle) (sqrt.f64 180))) (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))) 2))
	27.6b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (fma.f64 angle (.f64 (PI.f64) 1/180) (fma.f64 1/22674816000000 (.f64 (pow.f64 angle 5) (pow.f64 (PI.f64) 5)) (fma.f64 (pow.f64 (PI.f64) 7) (.f64 (pow.f64 angle 7) -1/30855889612800000000) (.f64 (pow.f64 (.f64 angle (PI.f64)) 3) -1/34992000))))) 2))

Compiler

Compiled 6506 to 4780 computations (26.5% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))
	0.3b	(pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)
	0.3b	(*.f64 (PI.f64) (/.f64 angle 180))
	24.4b	(sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))

series31.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

30.0ms

(*.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 20

Calls

1 calls:

7.0ms

(*.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))

simplify100.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

911×	`distribute-rgt-neg-in_binary64`
646×	`fma-neg_binary64`
509×	`associate-l_binary64`
452×	`associate-r_binary64`
412×	`distribute-lft-neg-in_binary64`

Counts

44 → 31

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	785
1	178	727
2	569	722
3	2006	713
4	3858	712
5	5218	712

prune849.0ms (2.9%)

Pruning

36 alts after pruning (36 fresh and 0 done)

	Pruned	Kept	Total
New	102	21	123
Fresh	19	15	34
Picked	1	0	1
Done	0	0	0
Total	122	36	158

Error

19.4b

Counts

158 → 36

Alt Table

Status	Error	Program
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 (PI.f64) (.f64 (cbrt.f64 180) (cbrt.f64 180))) (/.f64 angle (cbrt.f64 180))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	33.5b	(+.f64 (pow.f64 (.f64 a 1) 2) (-.f64 (.f64 1/32400 (.f64 (pow.f64 angle 2) (.f64 (pow.f64 (PI.f64) 2) (pow.f64 b 2)))) (.f64 1/3149280000 (.f64 (pow.f64 angle 4) (*.f64 (pow.f64 (PI.f64) 4) (pow.f64 b 2))))))
	30.4b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 angle 180)) 3)))) 2))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 (/.f64 angle 180))) (sqrt.f64 (/.f64 angle 180))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	33.5b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (.f64 b b) (-.f64 (.f64 (.f64 (.f64 angle angle) (pow.f64 (PI.f64) 2)) 1/32400) (.f64 (.f64 (pow.f64 angle 4) (pow.f64 (PI.f64) 4)) 1/3149280000))))
	20.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (cbrt.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 (/.f64 angle 180)) (cbrt.f64 (/.f64 angle 180)))) (cbrt.f64 (/.f64 angle 180))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
▶	20.7b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 angle (sqrt.f64 180))))) 2))
	44.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 (.f64 b (sqrt.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (sqrt.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) 2))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cbrt.f64 (.f64 (.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	43.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 angle) (sqrt.f64 180))) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (log.f64 (exp.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	37.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)))
	20.8b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (/.f64 (*.f64 angle (PI.f64)) 180))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (expm1.f64 (log1p.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (*.f64 (/.f64 angle 180) (cbrt.f64 (PI.f64)))))) 2))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (/.f64 (sqrt.f64 angle) (sqrt.f64 180))) (/.f64 (sqrt.f64 angle) (sqrt.f64 180))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	24.7b	(+.f64 (pow.f64 (.f64 a (cos.f64 (expm1.f64 (log1p.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.7b	(+.f64 (pow.f64 (.f64 a 1) 2) (exp.f64 (log.f64 (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 angle) (cbrt.f64 angle))) (/.f64 (cbrt.f64 angle) 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	20.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)) (cbrt.f64 (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))) (cbrt.f64 (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (*.f64 (cbrt.f64 (/.f64 angle 180)) (cbrt.f64 (/.f64 angle 180)))) (cbrt.f64 (/.f64 angle 180))))) 2))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 (.f64 (cbrt.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) (cbrt.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) 2))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (*.f64 (cbrt.f64 angle) (cbrt.f64 angle))) (/.f64 (cbrt.f64 angle) 180)))) 2))
	25.3b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (/.f64 (.f64 (cbrt.f64 angle) (cbrt.f64 angle)) (sqrt.f64 180))) (/.f64 (cbrt.f64 angle) (sqrt.f64 180))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	25.8b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (.f64 1/180 (*.f64 angle (PI.f64)))) 2))
	27.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64)))) 2)))
	25.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 1/180 (.f64 angle (.f64 (PI.f64) b))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	44.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 (/.f64 angle 180)))))) 2))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (/.f64 (*.f64 (cbrt.f64 angle) (cbrt.f64 angle)) (sqrt.f64 180))) (/.f64 (cbrt.f64 angle) (sqrt.f64 180))))) 2))

Compiler

Compiled 5055 to 3833 computations (24.2% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (.f64 b (sin.f64 (.f64 (*.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 angle (sqrt.f64 180))))) 2)
✓	0.3b	(/.f64 angle (sqrt.f64 180))
✓	0.3b	(.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 angle (sqrt.f64 180)))
✓	24.4b	(sin.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 angle (sqrt.f64 180))))

series267.0ms (0.9%)

Counts

4 → 48

Calls

4 calls:

165.0ms	(pow.f64 (.f64 b (sin.f64 (.f64 (*.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 angle (sqrt.f64 180))))) 2)
67.0ms	(.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 angle (sqrt.f64 180)))
17.0ms	(sin.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 angle (sqrt.f64 180))))
17.0ms	(/.f64 angle (sqrt.f64 180))

rewrite60.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-exp-log_binary64`
36×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`

Counts

4 → 126

Calls

4 calls:

23.0ms	(.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 angle (sqrt.f64 180)))
8.0ms	(pow.f64 (.f64 b (sin.f64 (.f64 (*.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 angle (sqrt.f64 180))))) 2)
7.0ms	(/.f64 angle (sqrt.f64 180))
6.0ms	(sin.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 angle (sqrt.f64 180))))

simplify175.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

561×	`associate-/r*_binary64`
489×	`fma-def_binary64`
325×	`fma-neg_binary64`
281×	`associate-l_binary64`
251×	`associate-/l/_binary64`

Counts

174 → 185

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	247	3321
1	593	3030
2	2229	2522
3	4443	2520
4	5061	2520

prune1.5s (5.1%)

Pruning

36 alts after pruning (36 fresh and 0 done)

	Pruned	Kept	Total
New	173	12	185
Fresh	11	24	35
Picked	1	0	1
Done	0	0	0
Total	185	36	221

Error

19.3b

Counts

221 → 36

Alt Table

Status	Error	Program
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	24.3b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (expm1.f64 (log1p.f64 (/.f64 angle (sqrt.f64 180))))))) 2))
	27.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (pow.f64 (sin.f64 (/.f64 (*.f64 angle (PI.f64)) (pow.f64 (sqrt.f64 180) 2))) 2) (pow.f64 b 2)))
	44.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 (/.f64 angle 180)))))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 (/.f64 (PI.f64) (sqrt.f64 180)) (.f64 (cbrt.f64 (sqrt.f64 180)) (cbrt.f64 (sqrt.f64 180)))) (/.f64 angle (cbrt.f64 (sqrt.f64 180)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 (PI.f64) (.f64 (cbrt.f64 180) (cbrt.f64 180))) (/.f64 angle (cbrt.f64 180))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	33.5b	(+.f64 (pow.f64 (.f64 a 1) 2) (-.f64 (.f64 1/32400 (.f64 (pow.f64 angle 2) (.f64 (pow.f64 (PI.f64) 2) (pow.f64 b 2)))) (.f64 1/3149280000 (.f64 (pow.f64 angle 4) (*.f64 (pow.f64 (PI.f64) 4) (pow.f64 b 2))))))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 (/.f64 angle 180))) (sqrt.f64 (/.f64 angle 180))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	33.5b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (.f64 b b) (-.f64 (.f64 (.f64 (.f64 angle angle) (pow.f64 (PI.f64) 2)) 1/32400) (.f64 (.f64 (pow.f64 angle 4) (pow.f64 (PI.f64) 4)) 1/3149280000))))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 (/.f64 angle 180)) (cbrt.f64 (/.f64 angle 180)))) (cbrt.f64 (/.f64 angle 180))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.6b	(+.f64 (pow.f64 (.f64 a 1) 2) (exp.f64 (log.f64 (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 angle (sqrt.f64 180))))) 2))))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cbrt.f64 (.f64 (.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	37.8b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (pow.f64 (.f64 (sin.f64 (/.f64 (.f64 angle (PI.f64)) 180)) b) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)))
	20.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 (.f64 (cbrt.f64 angle) (cbrt.f64 angle)) (sqrt.f64 (sqrt.f64 180)))) (/.f64 (cbrt.f64 angle) (sqrt.f64 (sqrt.f64 180)))))) 2))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (expm1.f64 (log1p.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (*.f64 (/.f64 angle 180) (cbrt.f64 (PI.f64)))))) 2))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (/.f64 (PI.f64) (sqrt.f64 180)) (*.f64 (cbrt.f64 (/.f64 angle (sqrt.f64 180))) (cbrt.f64 (/.f64 angle (sqrt.f64 180))))) (cbrt.f64 (/.f64 angle (sqrt.f64 180)))))) 2))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (/.f64 (sqrt.f64 angle) (sqrt.f64 180))) (/.f64 (sqrt.f64 angle) (sqrt.f64 180))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	24.7b	(+.f64 (pow.f64 (.f64 a (cos.f64 (expm1.f64 (log1p.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	20.8b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 (*.f64 (cbrt.f64 angle) (cbrt.f64 angle)) (/.f64 (sqrt.f64 180) (cbrt.f64 angle)))))) 2))
	20.8b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (.f64 1/180 angle)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 angle) (cbrt.f64 angle))) (/.f64 (cbrt.f64 angle) 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	20.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)) (cbrt.f64 (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))) (cbrt.f64 (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (*.f64 (cbrt.f64 (/.f64 angle 180)) (cbrt.f64 (/.f64 angle 180)))) (cbrt.f64 (/.f64 angle 180))))) 2))
	20.8b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (/.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) angle) (sqrt.f64 180)))) 2))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 (.f64 (cbrt.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) (cbrt.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (/.f64 (.f64 (cbrt.f64 angle) (cbrt.f64 angle)) (sqrt.f64 180))) (/.f64 (cbrt.f64 angle) (sqrt.f64 180))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	25.8b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (.f64 1/180 (*.f64 angle (PI.f64)))) 2))
	27.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64)))) 2)))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (.f64 (.f64 (cbrt.f64 (/.f64 angle (sqrt.f64 180))) (cbrt.f64 (/.f64 angle (sqrt.f64 180)))) (cbrt.f64 (/.f64 angle (sqrt.f64 180))))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (log.f64 (exp.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
▶	20.7b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (/.f64 (*.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180)))) 2))

Compiler

Compiled 7552 to 5994 computations (20.6% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (.f64 b (sin.f64 (/.f64 (.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180)))) 2)
	0.3b	(/.f64 angle (sqrt.f64 180))
✓	0.4b	(/.f64 (*.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180))
✓	24.4b	(sin.f64 (/.f64 (*.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180)))

series243.0ms (0.8%)

Counts

3 → 48

Calls

3 calls:

161.0ms

(pow.f64 (*.f64 b (sin.f64 (/.f64 (*.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180)))) 2)

66.0ms

(/.f64 (*.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180))

16.0ms

(sin.f64 (/.f64 (*.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180)))

rewrite34.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64`
12×	`add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 61

Calls

3 calls:

15.0ms

(/.f64 (*.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180))

8.0ms

(pow.f64 (*.f64 b (sin.f64 (/.f64 (*.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180)))) 2)

4.0ms

(sin.f64 (/.f64 (*.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180)))

simplify139.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

507×	`associate-/r*_binary64`
484×	`associate-*l/_binary64`
434×	`associate-*r/_binary64`
394×	`associate-/l/_binary64`
337×	`associate-/r/_binary64`

Counts

109 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	185	2311
1	456	1753
2	1503	1697
3	4911	1697
4	4931	1697

prune1.2s (4.2%)

Pruning

38 alts after pruning (38 fresh and 0 done)

	Pruned	Kept	Total
New	150	5	155
Fresh	2	33	35
Picked	1	0	1
Done	0	0	0
Total	153	38	191

Error

19.3b

Counts

191 → 38

Alt Table

Status	Error	Program
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 1/180 (.f64 angle (PI.f64))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	24.3b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (expm1.f64 (log1p.f64 (/.f64 angle (sqrt.f64 180))))))) 2))
	27.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (pow.f64 (sin.f64 (/.f64 (*.f64 angle (PI.f64)) (pow.f64 (sqrt.f64 180) 2))) 2) (pow.f64 b 2)))
	21.1b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (/.f64 (.f64 (PI.f64) (.f64 (*.f64 (cbrt.f64 (/.f64 angle (sqrt.f64 180))) (cbrt.f64 (/.f64 angle (sqrt.f64 180)))) (cbrt.f64 (/.f64 angle (sqrt.f64 180))))) (sqrt.f64 180)))) 2))
	44.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 (/.f64 angle 180)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 (PI.f64) (.f64 (cbrt.f64 180) (cbrt.f64 180))) (/.f64 angle (cbrt.f64 180))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	33.5b	(+.f64 (pow.f64 (.f64 a 1) 2) (-.f64 (.f64 1/32400 (.f64 (pow.f64 angle 2) (.f64 (pow.f64 (PI.f64) 2) (pow.f64 b 2)))) (.f64 1/3149280000 (.f64 (pow.f64 angle 4) (*.f64 (pow.f64 (PI.f64) 4) (pow.f64 b 2))))))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 (/.f64 angle 180))) (sqrt.f64 (/.f64 angle 180))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	33.5b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (.f64 b b) (-.f64 (.f64 (.f64 (.f64 angle angle) (pow.f64 (PI.f64) 2)) 1/32400) (.f64 (.f64 (pow.f64 angle 4) (pow.f64 (PI.f64) 4)) 1/3149280000))))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 (/.f64 angle 180)) (cbrt.f64 (/.f64 angle 180)))) (cbrt.f64 (/.f64 angle 180))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.6b	(+.f64 (pow.f64 (.f64 a 1) 2) (exp.f64 (log.f64 (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 angle (sqrt.f64 180))))) 2))))
	38.4b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (pow.f64 (.f64 b (sin.f64 (/.f64 (.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180)))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cbrt.f64 (.f64 (.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	37.8b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (pow.f64 (.f64 (sin.f64 (/.f64 (.f64 angle (PI.f64)) 180)) b) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)))
	21.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (expm1.f64 (log1p.f64 (pow.f64 (.f64 b (sin.f64 (/.f64 (*.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180)))) 2))))
	21.2b	(+.f64 (pow.f64 (.f64 a (log.f64 (exp.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (/.f64 (.f64 (/.f64 (PI.f64) (.f64 (cbrt.f64 (sqrt.f64 180)) (cbrt.f64 (sqrt.f64 180)))) (/.f64 angle (sqrt.f64 180))) (cbrt.f64 (sqrt.f64 180))))) 2))
	20.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 (.f64 (cbrt.f64 angle) (cbrt.f64 angle)) (sqrt.f64 (sqrt.f64 180)))) (/.f64 (cbrt.f64 angle) (sqrt.f64 (sqrt.f64 180)))))) 2))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (expm1.f64 (log1p.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (*.f64 (/.f64 angle 180) (cbrt.f64 (PI.f64)))))) 2))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (/.f64 (sqrt.f64 angle) (sqrt.f64 180))) (/.f64 (sqrt.f64 angle) (sqrt.f64 180))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	24.7b	(+.f64 (pow.f64 (.f64 a (cos.f64 (expm1.f64 (log1p.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	20.8b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (/.f64 (*.f64 (cbrt.f64 angle) (cbrt.f64 angle)) (/.f64 (sqrt.f64 180) (cbrt.f64 angle)))))) 2))
	20.8b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (.f64 1/180 angle)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 angle) (cbrt.f64 angle))) (/.f64 (cbrt.f64 angle) 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	20.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)) (cbrt.f64 (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))) (cbrt.f64 (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (*.f64 (cbrt.f64 (/.f64 angle 180)) (cbrt.f64 (/.f64 angle 180)))) (cbrt.f64 (/.f64 angle 180))))) 2))
	20.8b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (/.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) angle) (sqrt.f64 180)))) 2))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 (.f64 (cbrt.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) (cbrt.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (.f64 (PI.f64) (/.f64 (.f64 (cbrt.f64 angle) (cbrt.f64 angle)) (sqrt.f64 180))) (/.f64 (cbrt.f64 angle) (sqrt.f64 180))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	25.8b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (.f64 1/180 (*.f64 angle (PI.f64)))) 2))
	27.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64)))) 2)))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (PI.f64) (/.f64 1 (sqrt.f64 180))) (.f64 (.f64 (cbrt.f64 (/.f64 angle (sqrt.f64 180))) (cbrt.f64 (/.f64 angle (sqrt.f64 180)))) (cbrt.f64 (/.f64 angle (sqrt.f64 180))))))) 2))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180))) (cbrt.f64 (/.f64 (.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180)))) (cbrt.f64 (/.f64 (*.f64 (PI.f64) (/.f64 angle (sqrt.f64 180))) (sqrt.f64 180)))))) 2))

Compiler

Compiled 5340 to 4213 computations (21.1% saved)

regimes5.2s (18%)

Accuracy

Total 1.3b remaining (6.3%)

Threshold costs 0b (0%)

Counts

228 → 1

Compiler

Compiled 42399 to 34745 computations (18.1% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	32
1	26	32
2	25	32

end1.0ms (0%)

Compiler: Compiled 23 to 20 computations (13% saved)

sample13.5s (46.2%)

Algorithm

1×

intervals

Results

3.4s	1590×	body	1024	valid
2.9s	1379×	body	1024	invalid
1.5s	5070×	body	128	valid
1.1s	793×	body	512	valid
992.0ms	696×	body	512	invalid
545.0ms	168×	body	2048	valid
278.0ms	376×	body	256	valid
275.0ms	320×	body	256	invalid
193.0ms	649×	body	128	invalid
34.0ms	3×	body	4096	valid

Compiler

Compiled 1209 to 986 computations (18.4% saved)

Details

analyze3.9s (13.3%)

sample570.0ms (2%)

simplify152.0ms (0.5%)

prune5.0ms (0%)

localize28.0ms (0.1%)

series78.0ms (0.3%)

rewrite29.0ms (0.1%)

simplify163.0ms (0.6%)

prune833.0ms (2.9%)

localize22.0ms (0.1%)

series31.0ms (0.1%)

rewrite9.0ms (0%)

simplify100.0ms (0.3%)

prune849.0ms (2.9%)

localize28.0ms (0.1%)

series267.0ms (0.9%)

rewrite60.0ms (0.2%)

simplify175.0ms (0.6%)

prune1.5s (5.1%)

localize29.0ms (0.1%)

series243.0ms (0.8%)

rewrite34.0ms (0.1%)

simplify139.0ms (0.5%)

prune1.2s (4.2%)

regimes5.2s (18%)

simplify4.0ms (0%)

end1.0ms (0%)

sample13.5s (46.2%)

Profiling